How can I use the same external HD for two different MacBooks?

I have a MacBook OS X 10.6.8 Snow Leopard with the respective backups for this device (as well as many other programs and archives) saved in a Seagate external HD. Now I got myself a Macbook Air OS X 10.10.2 Yosemite but it don't seem to even recognize de external HD. How do I proceed to keep and eventually pass the data from my external HD to my new MacBook?

Thanks in advance for the help.